2013 4th IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe), October 6-9, Copenhagen
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A Modelica Power System Library for
Phasor Time-Domain Simulation
T. Bogodorova, Student Member, IEEE, M. Sabate, G. León,
L. Vanfretti, Member, IEEE, M. Halat, J. B. Heyberger, and P. Panciatici, Member, IEEE
Abstract— Power system phasor time-domain simulation is
often carried out through domain specific tools such as Eurostag,
PSS/E, and others. While these tools are efficient, their individual
sub-component models and solvers cannot be accessed by the
users for modification. One of the main goals of the FP7 iTesla
project [1] is to perform model validation, for which, a modelling
and simulation environment that provides model transparency
and extensibility is necessary. 1 To this end, a power system
library has been built using the Modelica language. This article
describes the Power Systems library, and the software-to-software
validation carried out for the implemented component as well as
the validation of small-scale power system models constructed
using different library components. Simulations from the Modelica models are compared with their Eurostag equivalents.
Finally, due to its standardization, the Modelica language is
supported by different modelling and simulation tools. This
article illustrates how Modelica models can be shared across
different simulation platforms without loss of information and
maintaining consistency in simulation results.
Index Terms—Power system simulation, model validation,
Modelica
I. I NTRODUCTION AND M OTIVATION
Several attempts of power systems modeling using the
Modelica language have been made [2], [3]. Nevertheless,
several of these libraries (e.g. [3]) have become proprietary
software and closed for modifications. The latter means one
can no longer determine which modelling simplifications have
been implemented by the authors during model development.
On the other hand, available open source libraries [4] are
not maintained in order to be compliant with the current
Modelica language standard. Such libraries require dramatic
changes from end users to support each new version of the
language. Due to these reasons the authors were urged to
make a new power system library that offered simplicity for
maintenance and extensibility. In general, an equation-based
modelling language is the most appropriate choice because
one will know the exact model of the system independently
of the software in which it is modelled. In the case of the
Modelica language, it allows for consistent model sharing between different simulation platforms supporting the Modelica
language.
Another reason for modelling of power systems using
Modelica is that it offers the possibility of exploiting powerful
mathematical or engineering tools as M ATLAB/Simulink,
Mathematica and JModelica.org, through the Flexible
Mock-up Interface (FMI) or inherently [5]. Within
M ATLAB/Simulink, Modelica models can be used through
1 This research was supported by the iTesla Collaborative R&D project cofunded by the European Commission (7th Framework Programme) [1].
the FMI Toolbox; while for Mathematica, SystemModeler
links Modelica models directly with the computation kernel.
The aims of this article is to demonstrate the value of
Modelica as a convenient language for modeling of complex
physical systems containing electric power subcomponents,
to show results of software-to-software validations in order
to demonstrate the capability of Modelica for supporting
phasor time-domain power system models, and to illustrate
how power system Modelica models can be shared across
different simulation platforms. In addition, several aspects of
using Modelica for simulation of complex power systems are
addressed:
• Design and implementation of new electrical and nonelectrical component blocks
• Connection of electrical and non-electrical components
• Modeling of different synchronous machines matching
Eurostag’s models
• Performing phasor time-domain simulations, studying
initialization for models and analysing system response
to time events.
The remainder of this article is organized as follows. Section II offers a description of the power system elementary
component models for electrical and non-electrical domains
included into the library. Section II is dedicated to validation of
the components incorporated into two power systems. Section
III shows a software-to-software validation of the new library
through the simulation of two test systems and comparison
with their Eurostag equivalents. Section IV demonstrates how
the use of Modelica allows to exploit different modeling
and simulation environments without ambiguity on the model
itself. In Section V, the results are summarized, conclusions
and the future work are presented.
II. A M ODELICA P OWER S YSTEMS L IBRARY
This section describes the power system library models
developed using the Modelica language. A previous version
of the library [2] was developed in Scilab/Xcos simulation
environment during the European project PEGASE (see [2]).
Scilab/Xcos has several limitations in the support of Modelica
language specification [6]. Therefore, for the iTesla project
each component block inherited from PEGASE into the Power
Systems library was converted from Scilab/Xcos models to the
most recent Modelica language definition by using Dymola.
The conversion involves creation of the Modelica classes into
Dymola including their graphical representation and utilizing
differential and algebraic equations corresponding to each
electrical or a block in the PEGASE library. The Power System
978-1-4799-2984-9/13/$31.00 ©2013 IEEE
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library has also been improved adding new electrical and
mathematical blocks. With these new components it is possible
to build and simulate power systems of small and medium size
using Modelica language, to perform time-domain simulations
and to validate results using Eurostag models as reference.
In the following section, the authors present the list of the
components (electrical and non-electrical) of the library with a
short description of their functionality, paying special attention
to new models that have been recently developed and omitting
descriptions of simple blocks. The next section (Section III)
shows two examples of power networks: a system with one
machine (“System A”), and another (“System B”) containing
two machines (with different levels of model complexity).
Simulations for both systems are carried out in Dymola and
compared against their corresponding simulations in Eurostag.
•
•
•
A. Electrical Blocks
New electrical blocks which are most frequently used for
power systems modeling were created. Several blocks were
translated from Scilab/Xcos [7] to Dymola with a list of
modifications presented below:
1) Creation of blocks for connector’s pin (PwPin) in
Dymola. This connector connects components electrically
(real and imaginary part of voltage and current)
2) Introduction of equations inside a Class for each component model, indicating the corresponding pins to be used
and defining Icons for each block
3) Adaptation of connector blocks to Modelica format
4) Putting all the new blocks in a single package named
Power System Library
5) Reviewing that parameters and variables were in accordance to Modelica formats
6) Checking all block models in Dymola to see if the number of equations and number of variables were correct,
implying that the translation was done correctly.
The modeled library now contains the following electrical
blocks:
• PwLine. The model of the transmission line is based
on the equivalent pi-model. It is represented by a series
impedance and two shunt impedances located at the two
terminal nodes.
• PwLoad. The load is modeled by an impedance between
it’s connection node and the ground.
• PwTransformer. The model is based on the transformer
equivalent circuit, composed of an ideal transformer, a
series impedance taking into account losses due to the
load current and a shunt admittance representing no-load
losses.
• PwGenerator. The modeling of synchronous machine is
done according to Park’s classical theory. The developed
model corresponds to Eurostag’s full model, given by
its internal parameters. For more detailed information
see [8], p.57.
• PwLinewithOpening. Power line with opening event
during certain period of time at a specific time t.
•
PwLoadWithVariation. This block describes a model
which similar to the PwLoad block from the PEGASE
library, but in this case the input values are the initial
voltage at the node and the active and reactive power
consumed by the load. This class allows a variation on
the active and/or reactive power at a specific time t.
PwCapacitorBank. The capacitor bank model is composed of a set of capacitors connected in parallel on a
node called steps, with the possibility to switch on (+) or
switch off (-) a certain number of steps at a certain time
t1 .
PwGeneratorM1S. A synchronous machine may be given
either by its internal parameters or by its external parameters. Given the external parameters, the record PwExtIntParameters computes the internal parameters, using the
Canay model [9] (if the Canay mutual inductance, and
the damper circuit time constant are not equal to 0).
PwGeneratorMS2. Once the internal parameters are
computed, the developed model PwGeneratorMS2 is
used.This model corresponds to Eurostag’s full model
( [8], p.74) given by its external parameters.
B. Non-Electrical Blocks
A collection of non-electrical blocks have been created in
order to model synchronous generator controls (AVR or PSS)
in a block-oriented fashion. Most of these models have been
adapted from the PEGASE library to Dymola, and some of
them have been developed for the modeling of the turbine
governor and the voltage regulator models in Eurostag [8].
These non-electrical blocks were designed to be compatible
with the input/output blocks from the Modelica standard
library.
III. S OFTWARE - TO - SOFTWARE VALIDATION OF
COMPONENT MODELS
The first system built to test the library, shown in (Fig. 1),
is called System A. It is composed by a 1000 MW unit,
a synchronous machine, feeding a 600 + j200 MVA load
through a 24/400 kV step-up transformer, two 400 kV lines
and a 400/158 kV transformer. Two events are simulated at
specific times to study the systems’ behavior after:
•
•
An instantaneous increase in the load of 50 + j25 MVA
at time t = 10 s.
Switching off one of the two 380 kV lines at the receiving
node at time t = 20 s.
Fig. 1: Dymola Diagram of System A
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The synchronous machine (Generator M2S in Eurostag) is
given by its external parameters and the PwExtIntParameters
block (not shown in the figure) computes the internal parameters. It is equipped with a voltage regulator chain that consists
of a constant excitation voltage, and a governor chain.
In order to validate System A, the same system has been
built and simulated in Eurostag. The start values necessary
for time simulations for the synchronous machines models,
voltage regulators, voltage governors and power loads are
taken from the result of the power flow computations and
dynamic initialization in Eurostag. Once these values are
known, the system can be simulated using Dymola.
A. System B
The second test system is called System B (Fig. 2) and
is composed by nodes NGEN, NHV1, NHV2 and NLOAD
similar to System A, and a new node NHV3 where a new
synchronous machine is connected. The 1000 MW machine
connected to node NGEN is defined by its internal parameters
(Eurostags machine M1S) and is regulated with the speed
governor GOVER3 and the voltage regulator AVR3. The node
NHV2 is linked by a 380kV line to the node NHV3 where
a second synchronous machine is connected. This machine
is also defined by its internal parameters, has an internal
transformer and is regulated by GOVER3 and AVR3 controller
models.
Fig. 3: Results of System A model validation
machine given by external parameters as well as the line
opening event and load with modification.
b) System B: After running the simulation in Eurostag
and Dymola, the voltage magnitude for the NGEN and the
NLOAD nodes obtained are shown in Fig. 4. The voltage drop
and the subsequent voltage stabilization after a change in the
compensation level of the capacitor bank can be observed.
Fig. 2: Dymola Diagram of System B
B. Validation against faults
a) System A: After running the simulation in Eurostag
and Dymola, the voltage magnitude for the NGEN and the
NLOAD nodes (Fig. 1) have been chosen as output for
validation. As can be seen from Fig. 3, there is an expected
voltage drop and the subsequent voltage stabilization after
an instantaneous increase in the load of 50 + j25 MVA at
time t = 10 s, and after switching off one of the two 380
kV lines at the receiving node at time t = 20 s. Obtaining
the same results for the time-simulations performed in the
two different environments demonstrates high accuracy of
models built using Modelica and validity of choice of the
equation-based language for construction of models of small
and medium size. The results serve as evidence of correctness
of the new component models in particular for the synchronous
Fig. 4: Results of System B model validation
Analyzing the result in Fig. 4, one can observe small
oscillations of Dymola model appeared at the initialization
phase that are not seen in Eurostag. This is probably due
to initialization of regulators from Eurostag values or other
parameters of System B. In order to solve this problem, tests
are performed in Dymola and Eurostag. One of the possible
solutions for the initial oscillation problem is to start the
simulation 3 seconds before to allow the Modelica solver reach
the steady-state. On the other hand the systems response to the
bank modification is similar in both tools, thus indicating that
the Modelica models are valid.
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IV. M ODELICA M ODEL E XCHANGE AND S IMULATION
ACROSS D IFFERENT S IMULATION E NVIRONMENTS
This section demonstrates the flexibility and benefits of
using Modelica for model exchange and simulation across
different software platforms supporting the Modelica language. Four different simulation environments have been chosen in order to test feasibility and compatibility of Modelica
models for exchange. SystemModeler can interpret the Modelica models directly, while the FMI Toolbox for M ATLAB
uses Flexible Mock-Up Units (FMUs) which is a software
component used to exchange Modelica models through the
FMI standard [10]. This allows the user to benefit from the
numerical computation, visualization and modeling capabilities of Mathematica, M ATLAB, or other tools. OpenModelica
and JModelica.org are open source software which also offer modeling and simulation capabilities compliant with the
Modelica language.
A. FMI Toolbox & M ATLAB/Simulink
FMI Toolbox was designed for model exchange purposes
via an individual executable model representation called Functional Mock-up Unit (FMU) [11]. FMUs facilitate model
exchange through two options:
• FMUs of specific devices are generated, and then incorporated into the overall model in M ATLAB/Simulink
• FMUs of a complete model can be generated and shared
without revealing the model’s internal structure/equations
As an example we explore the second option in this paper. For
this purpose the model of System A was chosen. FMUs can
be generated using Dymola, JModelica.org, and other tools.
The results in this paper were achieved using Dymola as
FMU compiler and the FMI Toolbox in M ATLAB/Simulink as
recipient of the FMU (Fig. 5). The simulation results obtained
Fig. 5: M ATLAB/Simulink model using FMI Toolbox
with M ATLAB/Simulink, Dymola, and Eurostag, respectively,
coincide with the results shown in Fig. 3.
B. System Modeler & Mathematica
Wolfram SystemModeler is a physical modeling and simulation tool. It can process the Modelica language, which
takes an advantage of the strengths from equation-based
modeling, where the flow in components is modeled. This
presents significant advantages compared to block-based
modeling [12]. In addition System Modeler is capable to
interpret Modelica models directly without conversion into
FMU. This ability makes it similar to Dymola, but the major
and decisive advantage of SystemModeler on Dymola is the
capability to use Mathematica - a well known computational
tool. The result of modelling (Fig. 6) and simulation (Fig. 7)
Fig. 6: SystemModeler model using the model in Fig. 1
is the same as using FMI Toolbox in M ATLAB/Simulink. The
only configuration that must be carried out is to load the Power
Systems Library in SystemModeler.
C. OpenModelica
OpenModelica is an open source Modelica-based modeling
and simulation environment. The goal with the OpenModelica
effort is to create a comprehensive open source Modelica
modeling, compilation and simulation environment based on
free software distributed in binary and source code form for
research, teaching, and industrial usage [13]. OpenModelica is
Open Source Software, and thus, it becomes attractive for nonprofit organizations (for example, universities) to exploit it. In
order to use models developed in Dymola in OpenModelica,
one should pay attention to any empty annotations. It may
generate errors, so just removing these annotations solves the
problem. As expected, the simulation result in OpenModelica
(Fig. 7) is identical to Dymola output (Fig. 3). It proves that the
model was transferred from Dymola to OpenModelica without
loss of information.
D. JModelica.org
JModelica.org is an Open Source Software whose main purpose is not only modelling and simulation, but also optimization [5]. Therefore the user can be interested in exploiting it
as free software for optimization purposes. The programming
language used by JModelica.org is Python.
JModelica.org allows users to simulate their own model or
use FMUs compiled in another software. In this paper the
second option was demonstrated, as shown in Fig. 8, one can
see the simulation results of System A.
V. C ONCLUSION AND F UTURE WORK
This article described a power system model library developed using the Modelica language, and the softwareto-software validation of the library components with respect to models in Eurostag. The possibility to build
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Fig. 8: JModelica.org simulation results
(a) OpenModelica simulation results
nents in order to simulate bigger systems.
Continue with the development of new components models to enlarge the Power System Library.
At the time of preparation of this paper, the library is
undergoing a continuous development of models. The iTesla
consortium partners are discussing the possibilities of publicly
releasing the library under an open source license. The release
of the library will most likely take place at the end of the FP7
iTesla project in 2015.
•
R EFERENCES
(b) SystemModeler simulation results
Fig. 7: OpenModelica and SystemModeler simulation results
power systems in different simulation environments was
investigated. An example model was transferred from
Dymola to M ATLAB/Simulink, SystemModeler/Mathematica,
OpenModelica, and JModelica.org (Figs. 3, 5, 7, 8). The
results of software-to-software validation have shown that the
model is interpreted correctly by each of the software tested.
The decision on which simulation environment to use is left
for the end user, thereby providing flexibility to use the power
system model in different computational environments. Future
work will consider the challenges enumerated below:
•
•
•
Validation of Eurostag’s induction machine model in
Modelica using a simple system.
Include initial equations to improve initialization.
Build and test new electrical and non-electrical compo-
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